The MCTM Elementary Math Contest: Who Participates and Who Wins?

Dr. David Ashley, dia059@smsu.edu math.smsu.edu/faculty/ashley.html

Dr. Lynda Plymate, lsm953f@smsu.edu

math.smsu.edu/~lyndaDepartment of Mathematics

Southwest Missouri State University

Springfield, MO 65804

Test Background• MCTM Annual Exam • 25 Regional Sites• Grades 4,5, and 6• Schools Select Participants 3-5/Grade Level

• Concepts Exam (24)Problem Solving (18)• Exams measure conceptual understanding

and problem solving ability. • The top three winners go to State.

Research Design/Methodology

• Regional survey (10 Items)

• Parent Survey (30 Items)

• Exam Analysis– Concept/Problem Solving– Conceptual/ Procedural– NCTM Content Standards

Number of Regional Participants for the Last Ten Years

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2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994

Year

Nu

mb

er

Who Participated in 2004?

• 2783 Contestants at 25 Sites4th Grade: 956 students

5th Grade: 939 students

6th Grade: 888 students

• 388 State Finalists4th Grade: 127 students

5th Grade: 132 students

6th Grade: 129 students

Regional Test ResultsRegional Concepts

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4

8

12

16

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24

Sc

ore

Grade4th 5th 6th

Regional Problem Solving

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3

6

9

12

15

18

Grade4th 5th 6th

State Finals Test Results

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4

8

12

16

20

24

Sc

ore

Grade4th 5th 6th

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3

6

9

12

15

18

Grade4th 5th 6th

State Concepts State Problem Solving

Regional Data Survey Results

% of 4th Grade Female s N=425 3.76 2.59 1.65 4.47 88.00 1.65 0.00

% of 4th Grade Males N =537 5.59 2.05 0.93 3.17 88.08 2.79 0.00

% of 5th Grade Female s N=406 2.46 2.46 0.49 4.19 91.13 1.48 38.67

% of 5th Grade Males N =561 1.96 2.67 1.60 3.03 90.91 1.43 44.21

% of 6th Grade Female s N=340 0.88 3.24 0.29 1.47 92.06 2.94 43.53

% of 6th Grade Males N =463 0.86 5.18 1.08 1.08 92.87 0.86 48.81

Amer. Indian

Asian Hisp. Black Af.Amer. White Other

Race Repeaters (Percent)

Regional Data Survey Results

% of 4th Grade Females N=425 11.06 12.24 43.06 72.47 37.65 11.29

% of 4th Grade Males N=537 10.80 11.36 41.34 75.42 39.11 12.29

% of 5th Grade Females N=406 11.08 12.32 45.57 70.69 40.15 13.30

% of 5th Grade Males N=561 11.59 12.30 40.82 66.84 45.28 14.26

% of 6th Grade Females N=340 7.35 14.12 45.00 61.47 44.12 20.00

% of 6th Grade Males N=463 9.94 12.31 39.96 56.37 52.70 16.85

Weakest NCTM Standard

Number Meas. Geom. AlgebraProb. Data

Prob.

Word

Regional Data Survey Results

% of 4th Grade Fe male s N=4 25 5.41 37.18 52.71 3.76 1.41

% of 4th Grade M ale s N =537 12.66 40.97 40.78 4.66 1.30

% of 5th Grade Fe male s N=4 06 6.16 32.51 58.37 4.68 0.25

% of 5th Grade M ale s N =561 11.59 42.78 42.78 2.85 0.71

% of 6th Grade Fe male s N=3 40 3.82 29.12 56.18 9.71 1.47

% of 6th Grade M ale s N =463 12.10 38.66 46.00 3.89 0.43

Confidence Levels

Top 3 Top 10Above Ave.

Below Ave.

Not Prepare

Informal Findings• From our parent survey, we found that there were no

significant differences on how males and females were selected for the contest (57% took preliminary tests) or prepared for the contest (75% spent 5-20 hours working with teachers, other students and family members).

• In all categories and on both regional and state exams, male participants outperformed (sometimes significantly) female participants.

Participants By Gender

43.6%56.2%4th

44.8%55.2%5th

43.6%56.1%6th

FemaleMaleRegional

12.5%87.5%6th

6.3%93.8%5th

12.5%87.5%4th

State Winners

28.5%64.2%6th

29%71%5th

32.4%67.6%4th

State Qualifiers

Part icipants by Gender

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10

20

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4th 5th 6th 4th 5th 6th 4th 5th 6th

Males

Females

Regional State State Winners

State Winners by Gender

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1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Year

Pe

rce

nt

Female

Male

Compare Gender Performance

4th Grade Regional Concepts

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10

20

30

1 4 710 13 16 19 22

Test Questions

Perc

enta

ge

Corre

ct

% of Males

% of Females

5th Grade Regional Concepts

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10

20

30

1 4 710 13 16 19 22

Test Questions

Perc

enta

ge

Corre

ct % of Males

% of Females

6th Grade Regional Problem Solving

05

101520

1 3 5 7 911 13 15 17

Test Questions

Perc

enta

ge

Corre

ct % of Males

% of Females

Looking at the Exam Content

• Compare performance between concept and problem solving abilities.

• Compare performance between conceptual (rich in relationships) and procedural (rules and language) knowledge (Hiebert, 1986).

• Compare performance between the 5 NCTM Content Standards.

Concepts vs. Problem Solving

• Concept exams were 2/3 “concepts” and 1/3 “problem solving”.

Ex. If a given square has a side 8 inches in length and you have to draw a square with four times the area of the given square, how many inches are in the length of a side of the square you have to draw?

Concepts vs. Problem Solving

• Problem solving exams were 3/4 “problem solving” and 1/4 “concepts”.

Ex. Four boys work together painting houses for the summer. For each house they get $256. If they work four months and their expenses are $152 per month, how many houses must they paint for each of them to have a $1000 at the end of the summer?

• Regional exams: Students averaged 59% correct on problem solving and 42% correct on concepts.

• State exams: This reversed, with 48% correct on concepts and 38% correct on problem solving.

Conceptual vs. Procedural Knowledge

• Both regional and state tests had a higher percent of conceptual questions (59%, 65%).

• Regional exams: Students did better on the procedural (47% correct) than conceptual (39% correct) questions.

• State exams: Performed on both was about 40% correct, with slight improvement by grade level (4th - 35%, 5th - 43%, and 6 - 53% correct).

• No significant differences between genders.

Mathematical Content in Exams

• Number/Operation: Reg (37%), State (28%).

Ex. Find the number of minutes in the month of March.

• Algebra/Thinking: Reg (21%), State (28%)Ex. Two small pizzas and one large pizza

cost the same as five small pizzas. If a small pizza costs $4, then what does a large pizza cost?

• Geometry: Regional (14%), State (16%)Ex. The mid-points of a square are

joined as shown. A fraction of the original square is shaded. What fractional part of the original square is shaded?

• Measurement: Regional (20%), State (23%)

Ex. Cheryl is mowing the football field. It is 100 yards long and 75 feet wide. What is

the area of this football field in square feet?

• Data/Probability: Reg (8%), State (6%)

Ex. The average monthly rainfall for 6 months was 28.5 inches. If it had rained 1 inch more each month, what would the average have been?

Regional Test Content

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Number Algebra Geometry Measure Data

State Test Content

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Number Algebra Geometry Measure Data

Regional Content Performance

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7080

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Number Algebra Geometry Measure Data

Content Standards

ConceptsProb lem Solving

Low Performance in Geometry, Measurement and Data

0102030405060708090

100

GeomMale

GeomFemale

MeasMale

MeasFemale

DataMale

DataFemale

Content Performance by Gender

4th5th6th

Hardest Problems on Regional Exams• 2/3 of them were concepts, not problem solving.

Example: How could you rewrite 12 x 5 + 12 x 8, using the distributive property?

• 71% measured conceptual knowledge.Example: If x is an odd number, how would you represent the odd number following it?

• Number/operation and measurement were again the content of the hardest questions.

Example: If the area of a 1 x 3 rectangle is increased by a factor of 16, what are all of the possible whole-number dimensions of the new rectangle?

Gender Issues Concerning Content• 6th grade females had more success with

number and operation (93.8%) on the regional concepts test than males (59.2%). For all other tests and content areas, females scored slightly lower than males.

Regional Number/Operation Performance

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4 Conc 4 Prob 5 Conc 5 Prob 6 Conc 6 Prob

Grade Level and Contest Exam

MalesFemales

Procedural Problem Solving (Females Shine) vs. Creative Problem Solving (Males Shine)

• A square piece of paper is folded in half along the diagonal. The area of the resulting triangle is 50 cm2. What was the perimeter of the original square?

• What is the smallest possible sum for all Wednesday dates in a 30-day month?

Questions Where Females Outperformed Males

• The following diagram represents what division fact?– *** *** ***– *** *** ***– *** *** ***

• Your teacher tells you to turn to the facing pages which sum to 405. To which pages do you turn?

• A 15 minute tape in an answering machine can record how many 18 second messages?

Questions Where Females Outperformed Males

• Mad King Ludwig had a castle with a moat around it. One could enter the castle yard over 3 different drawbridges. From the castle yard, one could enter the castle through 4 different gates. There were 5 different doors through which one could enter the throne room. How many different ways from outside the castle could one enter the throne room?

• Tyrel gave Tonisha half of his Pokemons. Tonisha gave half of these to Erin. Erin kept 8 of them and gave the remaining 10 to Seri. How many Pokemons did Tyrel give to Tonisha?

Questions Where Males Outperformed Females

• 2/3 of them were problem solving, not concepts.Example: What is the smallest positive whole number answer possible when you rearrange the following seven symbols, using each exactly once? ( x - ) 9 2 4

• There was an even split between conceptual and procedural knowledge.

• 36% of them involved numbers/operations, and another 27% of them involved measurement.

Example: Find the distance between the two points (3, 5) and (6, 4).

Gender Differences Involving Repeaters• For both 5th and 6th grade regional

contests, the percent of repeating male participants (38%, 43%) was higher than female repeaters (33%, 38%).

• 40% of both 5th and 6th grade state qualifiers had also qualified for state the previous year (45% males, 30% females). 40% of 6th grade state qualifiers had also qualified for state 2 years previous (43% male, 32% female).

Possible Reasons From Literature Review For Gender Differences

• The dominance of males in mathematical contests can discourage females from pursuing their interest in the subject.

• By the second grade students have already identified math and science as “male”.

• By third grade, females rated their own competence in mathematics lower than that of their male classmates, even when they received the same or better grades.

Possible Reasons From Literature Review For Gender Differences

• Young females gain less experience than males with core math concepts due to the kinds of toys geared toward each gender.

• From birth, female infants are discouraged from risk-taking and from exploring the world around them, whereas males are given toys that encourage small motor skills and spatial visualization skills, both necessary for later development in mathematics.

• The preferred learning style for females is working collaboratively rather than competitively, and that females would enjoy mathematics more and increase their time on task if it were taught in a cooperative setting.

Possible Reasons From Literature Review For Gender Differences

• Self-confidence (or lack thereof) may also be a strong contributing factor to why males are outperforming females on this contest.

• The mathematics curriculum at middle school emphasizes abstract concepts and spatial visualization, two skills that many females have not had much experience with in pre-school and primary levels.

• Studies point to parental and societal perceptions and teacher behavior and expectations as the main reasons that females select out of science and mathematics.

Sample Questions By Content Standard Number/Operation

• Put the following problems in order (listing the letter for each) according to the size of their answers, smallest first:a. 49.95 X 70b. 2.49 X 99.9c. 9.99 X 499d. 99.9 X 9.80099

• David has $500 in a savings account. If his money earns 6% interest at the end of each year, how much money will he have in total after collecting his interest for the 6th year?

Sample Questions By Content Standard Algebra/Algebraic Thinking

• If you multiply a one-digit number by 3, add 8, divide by 2, and subtract 6, you will get the number you started with back. What is the number?

• 0 => 2.1 => 4.3 => 8.5 => 12 If the same rule applied to every number, then 6 => ? .

• What temperature in Fahrenheit is equivalent to 35 degrees Centigrade?

Sample Questions By Content StandardGeometry

• Thirteen one-inch cubes are put together to form the T-figure below. The complete outside of the T-figure (including the bottom) is painted red and then separated into its individual cubes. How many of the cubes have exactly 4 red faces?

• Find the distance between the points (3,5) and (6,4) to the nearest hundredth.

Sample Questions By Content StandardMeasurement

• Cheryl is mowing a ball field. It is 125 yards long and 75 feet wide. What is the area of the ball field in square feet?

• When the circumference of a toy balloon is increased from 20 inches to 25 inches, the radius is increased by?

• A model car has a scale in which 1/4 inch represents 28 inches. If the completed model is 2 3/4 inches long, how long is the actual car?

Sample Questions By Content StandardData and Probability

A motorist drives through three sets of traffic lights every day. The probability that the motorist has to stop at the first set of lights is 0.4, at the second 0.6, and at the third 0.63. Each set of lights is independent of the others. Calculate the probability that the motorist does not have to stop at any of the lights.

What number should be added to the following set of data so that the mean, median, and mode will become the same number? 91, 93, 93, 95, 95, 98, 100

Reference list

Ashley, David I. & Plymate, Lynda (2004). Gender Differences in the Missouri State Elementary Math Contest. In the Missouri Journal of Mathematical Sciences. Volume 16. Number 1. Winter 2004 pp 40 – 50.

Plymate, Lynda & Ashley, David (2003). Elementary Mathematics Contests: Student Performance on Questions Which Reflect NCTM Standards. Teaching Children Mathematics. Vol. 10 Num. 3 Nov. pp 162-169.